Analytic continuation of weighted $q$-Genocchi numbers and polynomials
Commun. Korean Math. Soc. 2013 Vol. 28, No. 3, 457-462
https://doi.org/10.4134/CKMS.2013.28.3.457
Printed July 1, 2013
Serkan Araci, Mehmet Acikgoz, and Aynur G\"{u}rsul
University of Gaziantep, University of Gaziantep, University of Gaziantep
Abstract : In the present paper, we analyse analytic continuation of weighted $q$ -Genocchi numbers and polynomials. A novel formula for weighted $q$ -Genocchi-zeta function $\widetilde{\zeta }_{G,q}\left( s\mid \alpha \right) $ in terms of nested series of $\widetilde{\zeta }_{G,q}\left( n\mid \alpha \right) $ is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted $q$-Genocchi polynomials.
Keywords : Genocchi numbers and polynomials, $q$-Genocchi numbers and polynomials, weighted $q$-Genocchi numbers and polynomials, weighted $q$-Genocchi-zeta function
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